Camera calibration is a necessary step in three-dimensional (3D) computer vision in order to extract metric information from two-dimensional (2D) images. Much work has been done, starting in the photogrammetry community [1, 3], and more recently in computer vision [8, 7, 19, 6, 21, 20, 14, 5]. According to the dimension of the calibration objects, the aforementioned works can be classified into roughly three categories: (i) 3D reference object based calibration; (ii) 2D plane based calibration; and (iii) self-calibration.
Three-dimensional reference object based camera calibration is performed by observing a calibration object whose geometry in 3-D space is known with precision. The calibration object usually consists of two or three planes orthogonal to each other. Sometimes, a plane undergoing a precisely know translation is also used [19], which equivalently provides 3D reference points. These approaches require an expensive calibration apparatus, and an elaborate setup.
Two-dimensional plane based camera calibration, requires observations of a planar pattern shown in different orientations [22, 17]. This technique, however, does not lend itself to stereoscopic (or multiple) camera set-ups. For instance, if one camera is mounted in the front of a room and another in the back of a room, it extremely difficult, if not impossible, to simultaneously observe a number of different calibration objects, to calibrate the relative geometry between the multiple cameras. Of course, this could be performed if the calibration objects were made transparent, but then the equipment costs would be incrementally higher.
Self-calibration techniques do not use any calibration object. By moving a camera in a static scene, the rigidity of the scene provides in general two constraints [14, 13] on the cameras' internal parameters from one camera displacement by using image information alone. If images are taken by the same camera with fixed internal parameters, correspondences between three images are sufficient to recover both the internal and external parameters which allow us to reconstruct 3-D structure up to a similarity [10,12]. Although no calibration objects are necessary, a large number of parameters are estimated, resulting in very expensive computer-implemented computations and a larger percentage of calibration errors.
It is noted that in the preceding paragraphs, as well as the remainder of this specification, the description refers to various individual publications identified by numeric designator contained within a pair of brackets. For example, such a reference may be identified by reciting “reference [1]” or simply “[1]”. Multiple references will be identified by a pair of brackets containing more than one designator, for example, [2, 4]. A listing of the publications corresponding to each designator can be found at the end of the Detailed Description section.